library(pracma)
library(ggplot2)
library(animation)
library(gganimate)
library(dplyr)

#### Create complex set ####
    # Imaginary parts
    y <- seq(0, 100, len = 10001)
    
    # Complex vector
    z <- 0.5 + y * 1i
    
#### Evaluation of Zeta function ####
    # Real part
    real <- Re(zeta(z))
    
    # Imaginary part
    imaginary <- Im(zeta(z))

#### Plotting ####
    zeta_df <- data.frame(real = real,
                 imag = imaginary,
                 frame = 1:10001)
    
    g <- zeta_df %>% 
            ggplot(aes(x = real, y = imaginary, frame = frame)) +
                geom_path(size = 1.2, aes(cumulative = T)) +
                geom_point(size = 2, aes(x = 0, y = 0)) 
    gganimate(p = g, filename = "riemann.mp4", interval = 0.001, title_frame = F)